Estimation of mode shapes of beam-like structures by a moving lumped mass

Abstract

This paper presents a method to estimate mode shapes of beam like structures by using the acceleration of a moving lumped mass. In fact, the coupled frequencies of the vehicle-beam interaction system are time varying and the non-stationary instantaneous frequencies (IFs) contain information of mode shapes. The theoretical analysis in this paper shows that the mode shapes can be re-constructed by using the IFs; therefore, extracting mode shapes becomes a problem of IF estimation. A modified time-frequency analysis method based on weighted polynomial chirplet transform is developed to estimate the non-stationary IFs. Moreover, a new sampling algorithm based on accumulative measured energy is proposed to reconstruct the mode shapes, in which more data are sampled at the area with higher measured energy, making it more robust to noise. The proposed method is more convenient since only a lumped mass with a single accelerometer is required, and it is more practical because external exciter is not required, and the surface roughness can be the source of excitation. Numerical simulations and laboratory scale experiments have been carried out, which show that the proposed method performs well in extracting mode shapes, even if the travelling speed is high.